Existing data sets do not provide strong upper constraints on the extent of DM halo, allowing emission to reach to an arbitrarily extended radius. Usually the most conservative choice when determining truncation radius for the DM halo is to choose the outermost member star used to estimate the velocity dispersion profile in the dSph.
Moreover, due to our imperfect knowledge of the dwarfs and poorly constrained \(J\)  factors for dSphs, many different realizations of halo \(J\) -profiles are consistent with the same kinematic data. This leads to systematic uncertainty on the calculation of cross-section upper limits [1]}.
In Table REF  we show, for the dSphs analysed in this work, some of their most significant properties as well as the integrated \(J\)  factor values, calculated within a cone of half-angle of
\(\theta _{max}=\arcsin (r_{max}/D)\) , where \(r_{max}\)  is the distance from the center of the dwarf to its outermost member star [2]}.
